LMFDB - Embedded newform 4235.2.a.bk.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 67x^{6} - 110x^{5} - 132x^{4} + 168x^{3} + 94x^{2} - 54x - 11 $ x^10 - 2x^9 - 14x^8 + 26x^7 + 67x^6 - 110x^5 - 132x^4 + 168x^3 + 94x^2 - 54*x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.85511$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.85511 q^{2} -2.66752 q^{3} +1.44142 q^{4} +1.00000 q^{5} -4.94854 q^{6} -1.00000 q^{7} -1.03623 q^{8} +4.11568 q^{9} +O(q^{10})$	\(q+1.85511 q^{2} -2.66752 q^{3} +1.44142 q^{4} +1.00000 q^{5} -4.94854 q^{6} -1.00000 q^{7} -1.03623 q^{8} +4.11568 q^{9} +1.85511 q^{10} -3.84501 q^{12} -1.71849 q^{13} -1.85511 q^{14} -2.66752 q^{15} -4.80515 q^{16} -4.34045 q^{17} +7.63502 q^{18} -3.07736 q^{19} +1.44142 q^{20} +2.66752 q^{21} +1.16265 q^{23} +2.76417 q^{24} +1.00000 q^{25} -3.18798 q^{26} -2.97611 q^{27} -1.44142 q^{28} +10.0207 q^{29} -4.94854 q^{30} +5.20319 q^{31} -6.84160 q^{32} -8.05199 q^{34} -1.00000 q^{35} +5.93241 q^{36} -8.91230 q^{37} -5.70882 q^{38} +4.58411 q^{39} -1.03623 q^{40} +2.96125 q^{41} +4.94854 q^{42} +6.91343 q^{43} +4.11568 q^{45} +2.15684 q^{46} -1.25189 q^{47} +12.8179 q^{48} +1.00000 q^{49} +1.85511 q^{50} +11.5782 q^{51} -2.47706 q^{52} +2.96519 q^{53} -5.52099 q^{54} +1.03623 q^{56} +8.20892 q^{57} +18.5895 q^{58} -8.62817 q^{59} -3.84501 q^{60} +9.84936 q^{61} +9.65246 q^{62} -4.11568 q^{63} -3.08159 q^{64} -1.71849 q^{65} +0.429444 q^{67} -6.25640 q^{68} -3.10139 q^{69} -1.85511 q^{70} -2.04754 q^{71} -4.26479 q^{72} +3.45720 q^{73} -16.5333 q^{74} -2.66752 q^{75} -4.43575 q^{76} +8.50402 q^{78} +15.0681 q^{79} -4.80515 q^{80} -4.40821 q^{81} +5.49344 q^{82} -17.5342 q^{83} +3.84501 q^{84} -4.34045 q^{85} +12.8251 q^{86} -26.7304 q^{87} +1.17404 q^{89} +7.63502 q^{90} +1.71849 q^{91} +1.67586 q^{92} -13.8796 q^{93} -2.32240 q^{94} -3.07736 q^{95} +18.2501 q^{96} -4.33074 q^{97} +1.85511 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9	$ 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9} + 2 q^{10} - 4 q^{12} + 18 q^{13} - 2 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} + 12 q^{18} + 14 q^{19} + 12 q^{20} + 4 q^{21} - 4 q^{23} + 46 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{27} - 12 q^{28} + 36 q^{29} + 8 q^{30} - 18 q^{31} + 4 q^{32} - 32 q^{34} - 10 q^{35} + 22 q^{36} + 4 q^{37} + 18 q^{38} + 6 q^{40} + 38 q^{41} - 8 q^{42} + 6 q^{43} + 14 q^{45} + 28 q^{46} - 18 q^{47} + 16 q^{48} + 10 q^{49} + 2 q^{50} - 4 q^{51} + 26 q^{52} - 26 q^{53} + 2 q^{54} - 6 q^{56} + 22 q^{57} + 10 q^{58} - 14 q^{59} - 4 q^{60} + 60 q^{61} + 22 q^{62} - 14 q^{63} + 18 q^{65} - 10 q^{67} + 2 q^{68} - 8 q^{69} - 2 q^{70} - 54 q^{72} + 18 q^{73} - 20 q^{74} - 4 q^{75} + 38 q^{76} + 40 q^{78} + 40 q^{79} + 4 q^{80} + 18 q^{81} - 36 q^{82} + 2 q^{83} + 4 q^{84} + 4 q^{85} + 42 q^{86} - 32 q^{87} + 2 q^{89} + 12 q^{90} - 18 q^{91} - 64 q^{92} + 26 q^{93} - 68 q^{94} + 14 q^{95} + 28 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9 + 2 * q^10 - 4 * q^12 + 18 * q^13 - 2 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 + 12 * q^18 + 14 * q^19 + 12 * q^20 + 4 * q^21 - 4 * q^23 + 46 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^27 - 12 * q^28 + 36 * q^29 + 8 * q^30 - 18 * q^31 + 4 * q^32 - 32 * q^34 - 10 * q^35 + 22 * q^36 + 4 * q^37 + 18 * q^38 + 6 * q^40 + 38 * q^41 - 8 * q^42 + 6 * q^43 + 14 * q^45 + 28 * q^46 - 18 * q^47 + 16 * q^48 + 10 * q^49 + 2 * q^50 - 4 * q^51 + 26 * q^52 - 26 * q^53 + 2 * q^54 - 6 * q^56 + 22 * q^57 + 10 * q^58 - 14 * q^59 - 4 * q^60 + 60 * q^61 + 22 * q^62 - 14 * q^63 + 18 * q^65 - 10 * q^67 + 2 * q^68 - 8 * q^69 - 2 * q^70 - 54 * q^72 + 18 * q^73 - 20 * q^74 - 4 * q^75 + 38 * q^76 + 40 * q^78 + 40 * q^79 + 4 * q^80 + 18 * q^81 - 36 * q^82 + 2 * q^83 + 4 * q^84 + 4 * q^85 + 42 * q^86 - 32 * q^87 + 2 * q^89 + 12 * q^90 - 18 * q^91 - 64 * q^92 + 26 * q^93 - 68 * q^94 + 14 * q^95 + 28 * q^96 + 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.85511	1.31176	0.655879	−	0.754866i	$-0.272298\pi$
$2$	1.85511	1.31176	0.655879	+	0.754866i	$0.272298\pi$
$3$	−2.66752	−1.54010	−0.770048	−	0.637986i	$-0.779768\pi$
$3$	−2.66752	−1.54010	−0.770048	+	0.637986i	$0.779768\pi$
$4$	1.44142	0.720709
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.94854	−2.02023
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.03623	−0.366363
$9$	4.11568	1.37189
$10$	1.85511	0.586636
$11$	0	0
$11$	0	0
$12$	−3.84501	−1.10996
$13$	−1.71849	−0.476624	−0.238312	−	0.971189i	$-0.576594\pi$
$13$	−1.71849	−0.476624	−0.238312	+	0.971189i	$0.576594\pi$
$14$	−1.85511	−0.495798
$15$	−2.66752	−0.688752
$16$	−4.80515	−1.20129
$17$	−4.34045	−1.05271	−0.526357	−	0.850264i	$-0.676442\pi$
$17$	−4.34045	−1.05271	−0.526357	+	0.850264i	$0.676442\pi$
$18$	7.63502	1.79959
$19$	−3.07736	−0.705994	−0.352997	−	0.935624i	$-0.614837\pi$
$19$	−3.07736	−0.705994	−0.352997	+	0.935624i	$0.614837\pi$
$20$	1.44142	0.322311
$21$	2.66752	0.582101
$22$	0	0
$23$	1.16265	0.242429	0.121215	−	0.992626i	$-0.461321\pi$
$23$	1.16265	0.242429	0.121215	+	0.992626i	$0.461321\pi$
$24$	2.76417	0.564233
$25$	1.00000	0.200000
$26$	−3.18798	−0.625215
$27$	−2.97611	−0.572752
$28$	−1.44142	−0.272402
$29$	10.0207	1.86080	0.930398	−	0.366550i	$-0.119461\pi$
$29$	10.0207	1.86080	0.930398	+	0.366550i	$0.119461\pi$
$30$	−4.94854	−0.903475
$31$	5.20319	0.934520	0.467260	−	0.884120i	$-0.345241\pi$
$31$	5.20319	0.934520	0.467260	+	0.884120i	$0.345241\pi$
$32$	−6.84160	−1.20944
$33$	0	0
$34$	−8.05199	−1.38091
$35$	−1.00000	−0.169031
$36$	5.93241	0.988736
$37$	−8.91230	−1.46517	−0.732586	−	0.680674i	$-0.761687\pi$
$37$	−8.91230	−1.46517	−0.732586	+	0.680674i	$0.761687\pi$
$38$	−5.70882	−0.926093
$39$	4.58411	0.734046
$40$	−1.03623	−0.163842
$41$	2.96125	0.462470	0.231235	−	0.972898i	$-0.425723\pi$
$41$	2.96125	0.462470	0.231235	+	0.972898i	$0.425723\pi$
$42$	4.94854	0.763576
$43$	6.91343	1.05429	0.527144	−	0.849776i	$-0.323263\pi$
$43$	6.91343	1.05429	0.527144	+	0.849776i	$0.323263\pi$
$44$	0	0
$45$	4.11568	0.613529
$46$	2.15684	0.318008
$47$	−1.25189	−0.182608	−0.0913038	−	0.995823i	$-0.529103\pi$
$47$	−1.25189	−0.182608	−0.0913038	+	0.995823i	$0.529103\pi$
$48$	12.8179	1.85010
$49$	1.00000	0.142857
$50$	1.85511	0.262352
$51$	11.5782	1.62128
$52$	−2.47706	−0.343507
$53$	2.96519	0.407300	0.203650	−	0.979044i	$-0.434720\pi$
$53$	2.96519	0.407300	0.203650	+	0.979044i	$0.434720\pi$
$54$	−5.52099	−0.751312
$55$	0	0
$56$	1.03623	0.138472
$57$	8.20892	1.08730
$58$	18.5895	2.44091
$59$	−8.62817	−1.12329	−0.561646	−	0.827378i	$-0.689832\pi$
$59$	−8.62817	−1.12329	−0.561646	+	0.827378i	$0.689832\pi$
$60$	−3.84501	−0.496389
$61$	9.84936	1.26108	0.630541	−	0.776156i	$-0.282833\pi$
$61$	9.84936	1.26108	0.630541	+	0.776156i	$0.282833\pi$
$62$	9.65246	1.22586
$63$	−4.11568	−0.518527
$64$	−3.08159	−0.385199
$65$	−1.71849	−0.213153
$66$	0	0
$67$	0.429444	0.0524650	0.0262325	−	0.999656i	$-0.491649\pi$
$67$	0.429444	0.0524650	0.0262325	+	0.999656i	$0.491649\pi$
$68$	−6.25640	−0.758700
$69$	−3.10139	−0.373364
$70$	−1.85511	−0.221728
$71$	−2.04754	−0.242998	−0.121499	−	0.992592i	$-0.538770\pi$
$71$	−2.04754	−0.242998	−0.121499	+	0.992592i	$0.538770\pi$
$72$	−4.26479	−0.502611
$73$	3.45720	0.404635	0.202317	−	0.979320i	$-0.435153\pi$
$73$	3.45720	0.404635	0.202317	+	0.979320i	$0.435153\pi$
$74$	−16.5333	−1.92195
$75$	−2.66752	−0.308019
$76$	−4.43575	−0.508816
$77$	0	0
$78$	8.50402	0.962890
$79$	15.0681	1.69530	0.847649	−	0.530557i	$-0.178017\pi$
$79$	15.0681	1.69530	0.847649	+	0.530557i	$0.178017\pi$
$80$	−4.80515	−0.537232
$81$	−4.40821	−0.489801
$82$	5.49344	0.606649
$83$	−17.5342	−1.92463	−0.962317	−	0.271931i	$-0.912338\pi$
$83$	−17.5342	−1.92463	−0.962317	+	0.271931i	$0.912338\pi$
$84$	3.84501	0.419525
$85$	−4.34045	−0.470788
$86$	12.8251	1.38297
$87$	−26.7304	−2.86580
$88$	0	0
$89$	1.17404	0.124448	0.0622238	−	0.998062i	$-0.480181\pi$
$89$	1.17404	0.124448	0.0622238	+	0.998062i	$0.480181\pi$
$90$	7.63502	0.804802
$91$	1.71849	0.180147
$92$	1.67586	0.174721
$93$	−13.8796	−1.43925
$94$	−2.32240	−0.239537
$95$	−3.07736	−0.315730
$96$	18.2501	1.86265
$97$	−4.33074	−0.439720	−0.219860	−	0.975531i	$-0.570560\pi$
$97$	−4.33074	−0.439720	−0.219860	+	0.975531i	$0.570560\pi$
$98$	1.85511	0.187394
$99$	0	0
$100$	1.44142	0.144142
$101$	11.0945	1.10394	0.551972	−	0.833863i	$-0.313876\pi$
$101$	11.0945	1.10394	0.551972	+	0.833863i	$0.313876\pi$
$102$	21.4789	2.12673
$103$	−1.06178	−0.104620	−0.0523102	−	0.998631i	$-0.516658\pi$
$103$	−1.06178	−0.104620	−0.0523102	+	0.998631i	$0.516658\pi$
$104$	1.78075	0.174617
$105$	2.66752	0.260324
$106$	5.50074	0.534279
$107$	18.2462	1.76393	0.881965	−	0.471314i	$-0.156220\pi$
$107$	18.2462	1.76393	0.881965	+	0.471314i	$0.156220\pi$
$108$	−4.28981	−0.412787
$109$	−7.53824	−0.722032	−0.361016	−	0.932560i	$-0.617570\pi$
$109$	−7.53824	−0.722032	−0.361016	+	0.932560i	$0.617570\pi$
$110$	0	0
$111$	23.7738	2.25651
$112$	4.80515	0.454044
$113$	18.4530	1.73591	0.867957	−	0.496640i	$-0.165433\pi$
$113$	18.4530	1.73591	0.867957	+	0.496640i	$0.165433\pi$
$114$	15.2284	1.42627
$115$	1.16265	0.108418
$116$	14.4440	1.34109
$117$	−7.07276	−0.653877
$118$	−16.0062	−1.47349
$119$	4.34045	0.397888
$120$	2.76417	0.252333
$121$	0	0
$122$	18.2716	1.65423
$123$	−7.89921	−0.712248
$124$	7.49996	0.673516
$125$	1.00000	0.0894427
$126$	−7.63502	−0.680182
$127$	−11.0148	−0.977409	−0.488705	−	0.872449i	$-0.662530\pi$
$127$	−11.0148	−0.977409	−0.488705	+	0.872449i	$0.662530\pi$
$128$	7.96652	0.704148
$129$	−18.4417	−1.62370
$130$	−3.18798	−0.279605
$131$	8.09741	0.707474	0.353737	−	0.935345i	$-0.384911\pi$
$131$	8.09741	0.707474	0.353737	+	0.935345i	$0.384911\pi$
$132$	0	0
$133$	3.07736	0.266841
$134$	0.796665	0.0688213
$135$	−2.97611	−0.256142
$136$	4.49770	0.385675
$137$	19.8048	1.69204	0.846020	−	0.533151i	$-0.178992\pi$
$137$	19.8048	1.69204	0.846020	+	0.533151i	$0.178992\pi$
$138$	−5.75341	−0.489763
$139$	2.23144	0.189269	0.0946343	−	0.995512i	$-0.469832\pi$
$139$	2.23144	0.189269	0.0946343	+	0.995512i	$0.469832\pi$
$140$	−1.44142	−0.121822
$141$	3.33946	0.281233
$142$	−3.79840	−0.318754
$143$	0	0
$144$	−19.7765	−1.64804
$145$	10.0207	0.832174
$146$	6.41348	0.530783
$147$	−2.66752	−0.220014
$148$	−12.8463	−1.05596
$149$	11.6509	0.954478	0.477239	−	0.878773i	$-0.341638\pi$
$149$	11.6509	0.954478	0.477239	+	0.878773i	$0.341638\pi$
$150$	−4.94854	−0.404046
$151$	3.19583	0.260073	0.130036	−	0.991509i	$-0.458491\pi$
$151$	3.19583	0.260073	0.130036	+	0.991509i	$0.458491\pi$
$152$	3.18885	0.258650
$153$	−17.8639	−1.44421
$154$	0	0
$155$	5.20319	0.417930
$156$	6.60762	0.529033
$157$	6.20417	0.495147	0.247573	−	0.968869i	$-0.420367\pi$
$157$	6.20417	0.495147	0.247573	+	0.968869i	$0.420367\pi$
$158$	27.9530	2.22382
$159$	−7.90972	−0.627281
$160$	−6.84160	−0.540876
$161$	−1.16265	−0.0916296
$162$	−8.17770	−0.642501
$163$	14.8824	1.16568	0.582841	−	0.812587i	$-0.301941\pi$
$163$	14.8824	1.16568	0.582841	+	0.812587i	$0.301941\pi$
$164$	4.26840	0.333306
$165$	0	0
$166$	−32.5279	−2.52465
$167$	−15.9864	−1.23706	−0.618532	−	0.785760i	$-0.712272\pi$
$167$	−15.9864	−1.23706	−0.618532	+	0.785760i	$0.712272\pi$
$168$	−2.76417	−0.213260
$169$	−10.0468	−0.772830
$170$	−8.05199	−0.617560
$171$	−12.6654	−0.968549
$172$	9.96514	0.759835
$173$	20.8933	1.58849	0.794244	−	0.607598i	$-0.207867\pi$
$173$	20.8933	1.58849	0.794244	+	0.607598i	$0.207867\pi$
$174$	−49.5878	−3.75924
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	23.0158	1.72998
$178$	2.17796	0.163245
$179$	−0.677555	−0.0506428	−0.0253214	−	0.999679i	$-0.508061\pi$
$179$	−0.677555	−0.0506428	−0.0253214	+	0.999679i	$0.508061\pi$
$180$	5.93241	0.442176
$181$	22.1606	1.64718	0.823591	−	0.567185i	$-0.191967\pi$
$181$	22.1606	1.64718	0.823591	+	0.567185i	$0.191967\pi$
$182$	3.18798	0.236309
$183$	−26.2734	−1.94219
$184$	−1.20477	−0.0888170
$185$	−8.91230	−0.655245
$186$	−25.7482	−1.88795
$187$	0	0
$188$	−1.80450	−0.131607
$189$	2.97611	0.216480
$190$	−5.70882	−0.414161
$191$	15.5815	1.12744	0.563720	−	0.825966i	$-0.309370\pi$
$191$	15.5815	1.12744	0.563720	+	0.825966i	$0.309370\pi$
$192$	8.22023	0.593244
$193$	16.6786	1.20055	0.600277	−	0.799792i	$-0.295057\pi$
$193$	16.6786	1.20055	0.600277	+	0.799792i	$0.295057\pi$
$194$	−8.03398	−0.576806
$195$	4.58411	0.328275
$196$	1.44142	0.102958
$197$	19.5196	1.39071	0.695356	−	0.718666i	$-0.255247\pi$
$197$	19.5196	1.39071	0.695356	+	0.718666i	$0.255247\pi$
$198$	0	0
$199$	3.59941	0.255155	0.127578	−	0.991829i	$-0.459280\pi$
$199$	3.59941	0.255155	0.127578	+	0.991829i	$0.459280\pi$
$200$	−1.03623	−0.0732725
$201$	−1.14555	−0.0808011
$202$	20.5815	1.44811
$203$	−10.0207	−0.703315
$204$	16.6891	1.16847
$205$	2.96125	0.206823
$206$	−1.96971	−0.137237
$207$	4.78509	0.332587
$208$	8.25761	0.572562
$209$	0	0
$210$	4.94854	0.341482
$211$	−21.3260	−1.46815	−0.734073	−	0.679071i	$-0.762383\pi$
$211$	−21.3260	−1.46815	−0.734073	+	0.679071i	$0.762383\pi$
$212$	4.27408	0.293545
$213$	5.46185	0.374240
$214$	33.8487	2.31385
$215$	6.91343	0.471492
$216$	3.08393	0.209835
$217$	−5.20319	−0.353215
$218$	−13.9842	−0.947132
$219$	−9.22217	−0.623176
$220$	0	0
$221$	7.45902	0.501748
$222$	44.1028	2.95999
$223$	−22.4966	−1.50648	−0.753242	−	0.657744i	$-0.771511\pi$
$223$	−22.4966	−1.50648	−0.753242	+	0.657744i	$0.771511\pi$
$224$	6.84160	0.457124
$225$	4.11568	0.274379
$226$	34.2323	2.27710
$227$	0.543112	0.0360476	0.0180238	−	0.999838i	$-0.494263\pi$
$227$	0.543112	0.0360476	0.0180238	+	0.999838i	$0.494263\pi$
$228$	11.8325	0.783625
$229$	−13.9351	−0.920857	−0.460429	−	0.887697i	$-0.652304\pi$
$229$	−13.9351	−0.920857	−0.460429	+	0.887697i	$0.652304\pi$
$230$	2.15684	0.142218
$231$	0	0
$232$	−10.3837	−0.681726
$233$	−14.9119	−0.976908	−0.488454	−	0.872590i	$-0.662439\pi$
$233$	−14.9119	−0.976908	−0.488454	+	0.872590i	$0.662439\pi$
$234$	−13.1207	−0.857728
$235$	−1.25189	−0.0816646
$236$	−12.4368	−0.809566
$237$	−40.1946	−2.61092
$238$	8.05199	0.521933
$239$	−1.99080	−0.128774	−0.0643871	−	0.997925i	$-0.520509\pi$
$239$	−1.99080	−0.128774	−0.0643871	+	0.997925i	$0.520509\pi$
$240$	12.8179	0.827389
$241$	19.4059	1.25004	0.625021	−	0.780608i	$-0.285090\pi$
$241$	19.4059	1.25004	0.625021	+	0.780608i	$0.285090\pi$
$242$	0	0
$243$	20.6873	1.32709
$244$	14.1970	0.908873
$245$	1.00000	0.0638877
$246$	−14.6539	−0.934297
$247$	5.28841	0.336493
$248$	−5.39170	−0.342373
$249$	46.7730	2.96412
$250$	1.85511	0.117327
$251$	−13.5215	−0.853471	−0.426736	−	0.904376i	$-0.640337\pi$
$251$	−13.5215	−0.853471	−0.426736	+	0.904376i	$0.640337\pi$
$252$	−5.93241	−0.373707
$253$	0	0
$254$	−20.4337	−1.28212
$255$	11.5782	0.725058
$256$	20.9419	1.30887
$257$	−11.3011	−0.704941	−0.352471	−	0.935823i	$-0.614658\pi$
$257$	−11.3011	−0.704941	−0.352471	+	0.935823i	$0.614658\pi$
$258$	−34.2114	−2.12991
$259$	8.91230	0.553783
$260$	−2.47706	−0.153621
$261$	41.2420	2.55282
$262$	15.0216	0.928035
$263$	−15.4669	−0.953731	−0.476866	−	0.878976i	$-0.658227\pi$
$263$	−15.4669	−0.953731	−0.476866	+	0.878976i	$0.658227\pi$
$264$	0	0
$265$	2.96519	0.182150
$266$	5.70882	0.350030
$267$	−3.13177	−0.191661
$268$	0.619008	0.0378120
$269$	−28.7227	−1.75125	−0.875626	−	0.482989i	$-0.839551\pi$
$269$	−28.7227	−1.75125	−0.875626	+	0.482989i	$0.839551\pi$
$270$	−5.52099	−0.335997
$271$	17.9112	1.08803	0.544015	−	0.839075i	$-0.316903\pi$
$271$	17.9112	1.08803	0.544015	+	0.839075i	$0.316903\pi$
$272$	20.8565	1.26461
$273$	−4.58411	−0.277443
$274$	36.7400	2.21955
$275$	0	0
$276$	−4.47040	−0.269087
$277$	16.6512	1.00048	0.500238	−	0.865888i	$-0.333246\pi$
$277$	16.6512	1.00048	0.500238	+	0.865888i	$0.333246\pi$
$278$	4.13956	0.248274
$279$	21.4147	1.28206
$280$	1.03623	0.0619266
$281$	22.8496	1.36309	0.681546	−	0.731776i	$-0.261308\pi$
$281$	22.8496	1.36309	0.681546	+	0.731776i	$0.261308\pi$
$282$	6.19505	0.368910
$283$	−2.81831	−0.167531	−0.0837656	−	0.996485i	$-0.526695\pi$
$283$	−2.81831	−0.167531	−0.0837656	+	0.996485i	$0.526695\pi$
$284$	−2.95135	−0.175131
$285$	8.20892	0.486254
$286$	0	0
$287$	−2.96125	−0.174797
$288$	−28.1579	−1.65922
$289$	1.83950	0.108206
$290$	18.5895	1.09161
$291$	11.5523	0.677210
$292$	4.98327	0.291624
$293$	−6.31839	−0.369124	−0.184562	−	0.982821i	$-0.559087\pi$
$293$	−6.31839	−0.369124	−0.184562	+	0.982821i	$0.559087\pi$
$294$	−4.94854	−0.288605
$295$	−8.62817	−0.502351
$296$	9.23519	0.536785
$297$	0	0
$298$	21.6136	1.25204
$299$	−1.99800	−0.115547
$300$	−3.84501	−0.221992
$301$	−6.91343	−0.398484
$302$	5.92860	0.341153
$303$	−29.5948	−1.70018
$304$	14.7872	0.848102
$305$	9.84936	0.563973
$306$	−33.1394	−1.89446
$307$	21.6407	1.23510	0.617551	−	0.786531i	$-0.288125\pi$
$307$	21.6407	1.23510	0.617551	+	0.786531i	$0.288125\pi$
$308$	0	0
$309$	2.83232	0.161125
$310$	9.65246	0.548223
$311$	16.5006	0.935664	0.467832	−	0.883817i	$-0.345035\pi$
$311$	16.5006	0.935664	0.467832	+	0.883817i	$0.345035\pi$
$312$	−4.75020	−0.268927
$313$	−17.0814	−0.965496	−0.482748	−	0.875759i	$-0.660361\pi$
$313$	−17.0814	−0.965496	−0.482748	+	0.875759i	$0.660361\pi$
$314$	11.5094	0.649513
$315$	−4.11568	−0.231892
$316$	21.7195	1.22182
$317$	5.93686	0.333447	0.166724	−	0.986004i	$-0.446681\pi$
$317$	5.93686	0.333447	0.166724	+	0.986004i	$0.446681\pi$
$318$	−14.6734	−0.822841
$319$	0	0
$320$	−3.08159	−0.172266
$321$	−48.6723	−2.71662
$322$	−2.15684	−0.120196
$323$	13.3571	0.743209
$324$	−6.35407	−0.353004
$325$	−1.71849	−0.0953247
$326$	27.6085	1.52909
$327$	20.1084	1.11200
$328$	−3.06854	−0.169432
$329$	1.25189	0.0690192
$330$	0	0
$331$	16.7598	0.921203	0.460601	−	0.887607i	$-0.347634\pi$
$331$	16.7598	0.921203	0.460601	+	0.887607i	$0.347634\pi$
$332$	−25.2742	−1.38710
$333$	−36.6802	−2.01006
$334$	−29.6564	−1.62273
$335$	0.429444	0.0234631
$336$	−12.8179	−0.699271
$337$	−4.52164	−0.246309	−0.123155	−	0.992387i	$-0.539301\pi$
$337$	−4.52164	−0.246309	−0.123155	+	0.992387i	$0.539301\pi$
$338$	−18.6379	−1.01377
$339$	−49.2238	−2.67347
$340$	−6.25640	−0.339301
$341$	0	0
$342$	−23.4957	−1.27050
$343$	−1.00000	−0.0539949
$344$	−7.16391	−0.386252
$345$	−3.10139	−0.166973
$346$	38.7593	2.08371
$347$	−25.6230	−1.37552	−0.687758	−	0.725940i	$-0.741405\pi$
$347$	−25.6230	−1.37552	−0.687758	+	0.725940i	$0.741405\pi$
$348$	−38.5297	−2.06541
$349$	4.00876	0.214584	0.107292	−	0.994228i	$-0.465782\pi$
$349$	4.00876	0.214584	0.107292	+	0.994228i	$0.465782\pi$
$350$	−1.85511	−0.0991596
$351$	5.11441	0.272987
$352$	0	0
$353$	27.6744	1.47296	0.736481	−	0.676458i	$-0.236486\pi$
$353$	27.6744	1.47296	0.736481	+	0.676458i	$0.236486\pi$
$354$	42.6968	2.26931
$355$	−2.04754	−0.108672
$356$	1.69228	0.0896905
$357$	−11.5782	−0.612786
$358$	−1.25694	−0.0664311
$359$	−0.991675	−0.0523386	−0.0261693	−	0.999658i	$-0.508331\pi$
$359$	−0.991675	−0.0523386	−0.0261693	+	0.999658i	$0.508331\pi$
$360$	−4.26479	−0.224774
$361$	−9.52988	−0.501572
$362$	41.1102	2.16070
$363$	0	0
$364$	2.47706	0.129833
$365$	3.45720	0.180958
$366$	−48.7400	−2.54768
$367$	−11.7872	−0.615286	−0.307643	−	0.951502i	$-0.599540\pi$
$367$	−11.7872	−0.615286	−0.307643	+	0.951502i	$0.599540\pi$
$368$	−5.58670	−0.291227
$369$	12.1876	0.634460
$370$	−16.5333	−0.859523
$371$	−2.96519	−0.153945
$372$	−20.0063	−1.03728
$373$	12.1466	0.628929	0.314465	−	0.949269i	$-0.398175\pi$
$373$	12.1466	0.628929	0.314465	+	0.949269i	$0.398175\pi$
$374$	0	0
$375$	−2.66752	−0.137750
$376$	1.29725	0.0669006
$377$	−17.2205	−0.886900
$378$	5.52099	0.283969
$379$	−35.6707	−1.83228	−0.916140	−	0.400858i	$-0.868712\pi$
$379$	−35.6707	−1.83228	−0.916140	+	0.400858i	$0.868712\pi$
$380$	−4.43575	−0.227549
$381$	29.3823	1.50530
$382$	28.9054	1.47893
$383$	−33.3602	−1.70463	−0.852313	−	0.523032i	$-0.824801\pi$
$383$	−33.3602	−1.70463	−0.852313	+	0.523032i	$0.824801\pi$
$384$	−21.2509	−1.08445
$385$	0	0
$386$	30.9406	1.57484
$387$	28.4535	1.44637
$388$	−6.24240	−0.316910
$389$	−33.0594	−1.67618	−0.838089	−	0.545534i	$-0.816327\pi$
$389$	−33.0594	−1.67618	−0.838089	+	0.545534i	$0.816327\pi$
$390$	8.50402	0.430618
$391$	−5.04642	−0.255208
$392$	−1.03623	−0.0523375
$393$	−21.6000	−1.08958
$394$	36.2109	1.82428
$395$	15.0681	0.758161
$396$	0	0
$397$	−14.3104	−0.718218	−0.359109	−	0.933296i	$-0.616919\pi$
$397$	−14.3104	−0.718218	−0.359109	+	0.933296i	$0.616919\pi$
$398$	6.67728	0.334702
$399$	−8.20892	−0.410960
$400$	−4.80515	−0.240258
$401$	24.3007	1.21352	0.606760	−	0.794885i	$-0.292469\pi$
$401$	24.3007	1.21352	0.606760	+	0.794885i	$0.292469\pi$
$402$	−2.12512	−0.105991
$403$	−8.94163	−0.445414
$404$	15.9918	0.795621
$405$	−4.40821	−0.219046
$406$	−18.5895	−0.922579
$407$	0	0
$408$	−11.9977	−0.593976
$409$	−5.68547	−0.281128	−0.140564	−	0.990072i	$-0.544892\pi$
$409$	−5.68547	−0.281128	−0.140564	+	0.990072i	$0.544892\pi$
$410$	5.49344	0.271302
$411$	−52.8298	−2.60590
$412$	−1.53047	−0.0754008
$413$	8.62817	0.424564
$414$	8.87685	0.436273
$415$	−17.5342	−0.860722
$416$	11.7572	0.576446
$417$	−5.95243	−0.291492
$418$	0	0
$419$	−6.18462	−0.302138	−0.151069	−	0.988523i	$-0.548272\pi$
$419$	−6.18462	−0.302138	−0.151069	+	0.988523i	$0.548272\pi$
$420$	3.84501	0.187617
$421$	19.7191	0.961049	0.480524	−	0.876981i	$-0.340446\pi$
$421$	19.7191	0.961049	0.480524	+	0.876981i	$0.340446\pi$
$422$	−39.5621	−1.92585
$423$	−5.15240	−0.250518
$424$	−3.07262	−0.149220
$425$	−4.34045	−0.210543
$426$	10.1323	0.490912
$427$	−9.84936	−0.476644
$428$	26.3004	1.27128
$429$	0	0
$430$	12.8251	0.618484
$431$	−38.9961	−1.87838	−0.939188	−	0.343403i	$-0.888420\pi$
$431$	−38.9961	−1.87838	−0.939188	+	0.343403i	$0.888420\pi$
$432$	14.3006	0.688040
$433$	−32.9149	−1.58179	−0.790894	−	0.611953i	$-0.790384\pi$
$433$	−32.9149	−1.58179	−0.790894	+	0.611953i	$0.790384\pi$
$434$	−9.65246	−0.463333
$435$	−26.7304	−1.28163
$436$	−10.8657	−0.520375
$437$	−3.57789	−0.171153
$438$	−17.1081	−0.817457
$439$	16.7771	0.800727	0.400364	−	0.916356i	$-0.368884\pi$
$439$	16.7771	0.800727	0.400364	+	0.916356i	$0.368884\pi$
$440$	0	0
$441$	4.11568	0.195985
$442$	13.8373	0.658172
$443$	28.1422	1.33707	0.668537	−	0.743679i	$-0.266921\pi$
$443$	28.1422	1.33707	0.668537	+	0.743679i	$0.266921\pi$
$444$	34.2679	1.62628
$445$	1.17404	0.0556547
$446$	−41.7336	−1.97614
$447$	−31.0790	−1.46999
$448$	3.08159	0.145592
$449$	34.3659	1.62183	0.810913	−	0.585167i	$-0.198971\pi$
$449$	34.3659	1.62183	0.810913	+	0.585167i	$0.198971\pi$
$450$	7.63502	0.359918
$451$	0	0
$452$	26.5985	1.25109
$453$	−8.52495	−0.400537
$454$	1.00753	0.0472858
$455$	1.71849	0.0805641
$456$	−8.50633	−0.398345
$457$	11.7707	0.550611	0.275305	−	0.961357i	$-0.411221\pi$
$457$	11.7707	0.550611	0.275305	+	0.961357i	$0.411221\pi$
$458$	−25.8511	−1.20794
$459$	12.9176	0.602943
$460$	1.67586	0.0781375
$461$	15.1852	0.707247	0.353623	−	0.935388i	$-0.384949\pi$
$461$	15.1852	0.707247	0.353623	+	0.935388i	$0.384949\pi$
$462$	0	0
$463$	−15.6463	−0.727143	−0.363572	−	0.931566i	$-0.618443\pi$
$463$	−15.6463	−0.727143	−0.363572	+	0.931566i	$0.618443\pi$
$464$	−48.1510	−2.23535
$465$	−13.8796	−0.643652
$466$	−27.6631	−1.28147
$467$	−2.01412	−0.0932023	−0.0466012	−	0.998914i	$-0.514839\pi$
$467$	−2.01412	−0.0932023	−0.0466012	+	0.998914i	$0.514839\pi$
$468$	−10.1948	−0.471255
$469$	−0.429444	−0.0198299
$470$	−2.32240	−0.107124
$471$	−16.5498	−0.762573
$472$	8.94077	0.411532
$473$	0	0
$474$	−74.5653	−3.42490
$475$	−3.07736	−0.141199
$476$	6.25640	0.286762
$477$	12.2038	0.558773
$478$	−3.69315	−0.168921
$479$	2.33033	0.106476	0.0532378	−	0.998582i	$-0.483046\pi$
$479$	2.33033	0.106476	0.0532378	+	0.998582i	$0.483046\pi$
$480$	18.2501	0.833001
$481$	15.3157	0.698336
$482$	36.0000	1.63975
$483$	3.10139	0.141118
$484$	0	0
$485$	−4.33074	−0.196649
$486$	38.3772	1.74082
$487$	−20.2787	−0.918915	−0.459458	−	0.888200i	$-0.651956\pi$
$487$	−20.2787	−0.918915	−0.459458	+	0.888200i	$0.651956\pi$
$488$	−10.2062	−0.462013
$489$	−39.6992	−1.79526
$490$	1.85511	0.0838051
$491$	−28.3830	−1.28090	−0.640452	−	0.767998i	$-0.721253\pi$
$491$	−28.3830	−1.28090	−0.640452	+	0.767998i	$0.721253\pi$
$492$	−11.3861	−0.513323
$493$	−43.4943	−1.95889
$494$	9.81056	0.441398
$495$	0	0
$496$	−25.0021	−1.12263
$497$	2.04754	0.0918445
$498$	86.7689	3.88821
$499$	22.9306	1.02651	0.513257	−	0.858235i	$-0.328439\pi$
$499$	22.9306	1.02651	0.513257	+	0.858235i	$0.328439\pi$
$500$	1.44142	0.0644621
$501$	42.6441	1.90520
$502$	−25.0839	−1.11955
$503$	−20.6091	−0.918914	−0.459457	−	0.888200i	$-0.651956\pi$
$503$	−20.6091	−0.918914	−0.459457	+	0.888200i	$0.651956\pi$
$504$	4.26479	0.189969
$505$	11.0945	0.493698
$506$	0	0
$507$	26.8000	1.19023
$508$	−15.8770	−0.704427
$509$	10.8253	0.479822	0.239911	−	0.970795i	$-0.422882\pi$
$509$	10.8253	0.479822	0.239911	+	0.970795i	$0.422882\pi$
$510$	21.4789	0.951101
$511$	−3.45720	−0.152938
$512$	22.9164	1.01277
$513$	9.15854	0.404359
$514$	−20.9647	−0.924712
$515$	−1.06178	−0.0467876
$516$	−26.5822	−1.17022
$517$	0	0
$518$	16.5333	0.726429
$519$	−55.7334	−2.44642
$520$	1.78075	0.0780911
$521$	20.9586	0.918212	0.459106	−	0.888382i	$-0.348170\pi$
$521$	20.9586	0.918212	0.459106	+	0.888382i	$0.348170\pi$
$522$	76.5083	3.34868
$523$	40.2786	1.76126	0.880629	−	0.473806i	$-0.157120\pi$
$523$	40.2786	1.76126	0.880629	+	0.473806i	$0.157120\pi$
$524$	11.6717	0.509883
$525$	2.66752	0.116420
$526$	−28.6928	−1.25106
$527$	−22.5842	−0.983782
$528$	0	0
$529$	−21.6482	−0.941228
$530$	5.50074	0.238937
$531$	−35.5108	−1.54104
$532$	4.43575	0.192314
$533$	−5.08889	−0.220424
$534$	−5.80977	−0.251413
$535$	18.2462	0.788854
$536$	−0.445003	−0.0192212
$537$	1.80739	0.0779948
$538$	−53.2836	−2.29722
$539$	0	0
$540$	−4.28981	−0.184604
$541$	−17.8824	−0.768824	−0.384412	−	0.923162i	$-0.625596\pi$
$541$	−17.8824	−0.768824	−0.384412	+	0.923162i	$0.625596\pi$
$542$	33.2273	1.42723
$543$	−59.1138	−2.53682
$544$	29.6956	1.27319
$545$	−7.53824	−0.322903
$546$	−8.50402	−0.363938
$547$	−1.18756	−0.0507766	−0.0253883	−	0.999678i	$-0.508082\pi$
$547$	−1.18756	−0.0507766	−0.0253883	+	0.999678i	$0.508082\pi$
$548$	28.5470	1.21947
$549$	40.5368	1.73007
$550$	0	0
$551$	−30.8373	−1.31371
$552$	3.21376	0.136787
$553$	−15.0681	−0.640763
$554$	30.8898	1.31238
$555$	23.7738	1.00914
$556$	3.21644	0.136407
$557$	4.24343	0.179800	0.0899000	−	0.995951i	$-0.471345\pi$
$557$	4.24343	0.179800	0.0899000	+	0.995951i	$0.471345\pi$
$558$	39.7264	1.68175
$559$	−11.8807	−0.502499
$560$	4.80515	0.203055
$561$	0	0
$562$	42.3884	1.78805
$563$	−29.3358	−1.23636	−0.618179	−	0.786038i	$-0.712129\pi$
$563$	−29.3358	−1.23636	−0.618179	+	0.786038i	$0.712129\pi$
$564$	4.81355	0.202687
$565$	18.4530	0.776324
$566$	−5.22826	−0.219760
$567$	4.40821	0.185128
$568$	2.12172	0.0890253
$569$	36.5737	1.53325	0.766624	−	0.642096i	$-0.221935\pi$
$569$	36.5737	1.53325	0.766624	+	0.642096i	$0.221935\pi$
$570$	15.2284	0.637848
$571$	−17.3937	−0.727905	−0.363952	−	0.931418i	$-0.618573\pi$
$571$	−17.3937	−0.727905	−0.363952	+	0.931418i	$0.618573\pi$
$572$	0	0
$573$	−41.5641	−1.73637
$574$	−5.49344	−0.229292
$575$	1.16265	0.0484858
$576$	−12.6829	−0.528453
$577$	−9.10038	−0.378854	−0.189427	−	0.981895i	$-0.560663\pi$
$577$	−9.10038	−0.378854	−0.189427	+	0.981895i	$0.560663\pi$
$578$	3.41246	0.141940
$579$	−44.4907	−1.84897
$580$	14.4440	0.599755
$581$	17.5342	0.727443
$582$	21.4308	0.888336
$583$	0	0
$584$	−3.58246	−0.148243
$585$	−7.07276	−0.292423
$586$	−11.7213	−0.484201
$587$	13.3182	0.549700	0.274850	−	0.961487i	$-0.411372\pi$
$587$	13.3182	0.549700	0.274850	+	0.961487i	$0.411372\pi$
$588$	−3.84501	−0.158566
$589$	−16.0121	−0.659765
$590$	−16.0062	−0.658963
$591$	−52.0689	−2.14183
$592$	42.8249	1.76009
$593$	24.4327	1.00333	0.501665	−	0.865062i	$-0.332721\pi$
$593$	24.4327	1.00333	0.501665	+	0.865062i	$0.332721\pi$
$594$	0	0
$595$	4.34045	0.177941
$596$	16.7938	0.687901
$597$	−9.60151	−0.392963
$598$	−3.70650	−0.151570
$599$	−20.4872	−0.837086	−0.418543	−	0.908197i	$-0.637459\pi$
$599$	−20.4872	−0.837086	−0.418543	+	0.908197i	$0.637459\pi$
$600$	2.76417	0.112847
$601$	−35.4291	−1.44518	−0.722591	−	0.691276i	$-0.757049\pi$
$601$	−35.4291	−1.44518	−0.722591	+	0.691276i	$0.757049\pi$
$602$	−12.8251	−0.522714
$603$	1.76746	0.0719764
$604$	4.60652	0.187437
$605$	0	0
$606$	−54.9015	−2.23022
$607$	8.44512	0.342777	0.171388	−	0.985204i	$-0.445175\pi$
$607$	8.44512	0.342777	0.171388	+	0.985204i	$0.445175\pi$
$608$	21.0541	0.853855
$609$	26.7304	1.08317
$610$	18.2716	0.739796
$611$	2.15137	0.0870351
$612$	−25.7493	−1.04086
$613$	3.25919	0.131637	0.0658187	−	0.997832i	$-0.479034\pi$
$613$	3.25919	0.131637	0.0658187	+	0.997832i	$0.479034\pi$
$614$	40.1458	1.62015
$615$	−7.89921	−0.318527
$616$	0	0
$617$	−25.5971	−1.03050	−0.515250	−	0.857040i	$-0.672301\pi$
$617$	−25.5971	−1.03050	−0.515250	+	0.857040i	$0.672301\pi$
$618$	5.25426	0.211357
$619$	20.4248	0.820942	0.410471	−	0.911874i	$-0.365364\pi$
$619$	20.4248	0.820942	0.410471	+	0.911874i	$0.365364\pi$
$620$	7.49996	0.301206
$621$	−3.46017	−0.138852
$622$	30.6104	1.22736
$623$	−1.17404	−0.0470368
$624$	−22.0274	−0.881800
$625$	1.00000	0.0400000
$626$	−31.6878	−1.26650
$627$	0	0
$628$	8.94280	0.356856
$629$	38.6834	1.54241
$630$	−7.63502	−0.304187
$631$	4.03675	0.160701	0.0803503	−	0.996767i	$-0.474396\pi$
$631$	4.03675	0.160701	0.0803503	+	0.996767i	$0.474396\pi$
$632$	−15.6141	−0.621094
$633$	56.8877	2.26108
$634$	11.0135	0.437402
$635$	−11.0148	−0.437111
$636$	−11.4012	−0.452087
$637$	−1.71849	−0.0680891
$638$	0	0
$639$	−8.42700	−0.333367
$640$	7.96652	0.314904
$641$	6.47732	0.255839	0.127919	−	0.991785i	$-0.459170\pi$
$641$	6.47732	0.255839	0.127919	+	0.991785i	$0.459170\pi$
$642$	−90.2922	−3.56355
$643$	−17.4010	−0.686229	−0.343115	−	0.939294i	$-0.611482\pi$
$643$	−17.4010	−0.686229	−0.343115	+	0.939294i	$0.611482\pi$
$644$	−1.67586	−0.0660382
$645$	−18.4417	−0.726143
$646$	24.7788	0.974911
$647$	9.96134	0.391620	0.195810	−	0.980642i	$-0.437266\pi$
$647$	9.96134	0.391620	0.195810	+	0.980642i	$0.437266\pi$
$648$	4.56792	0.179445
$649$	0	0
$650$	−3.18798	−0.125043
$651$	13.8796	0.543985
$652$	21.4518	0.840117
$653$	−2.68911	−0.105233	−0.0526165	−	0.998615i	$-0.516756\pi$
$653$	−2.68911	−0.105233	−0.0526165	+	0.998615i	$0.516756\pi$
$654$	37.3033	1.45867
$655$	8.09741	0.316392
$656$	−14.2293	−0.555560
$657$	14.2287	0.555116
$658$	2.32240	0.0905365
$659$	30.1592	1.17484	0.587418	−	0.809283i	$-0.300144\pi$
$659$	30.1592	1.17484	0.587418	+	0.809283i	$0.300144\pi$
$660$	0	0
$661$	−29.6842	−1.15458	−0.577292	−	0.816538i	$-0.695890\pi$
$661$	−29.6842	−1.15458	−0.577292	+	0.816538i	$0.695890\pi$
$662$	31.0912	1.20840
$663$	−19.8971	−0.772740
$664$	18.1695	0.705114
$665$	3.07736	0.119335
$666$	−68.0456	−2.63671
$667$	11.6506	0.451111
$668$	−23.0431	−0.891563
$669$	60.0102	2.32013
$670$	0.796665	0.0307778
$671$	0	0
$672$	−18.2501	−0.704014
$673$	42.9826	1.65686	0.828428	−	0.560095i	$-0.189235\pi$
$673$	42.9826	1.65686	0.828428	+	0.560095i	$0.189235\pi$
$674$	−8.38812	−0.323098
$675$	−2.97611	−0.114550
$676$	−14.4816	−0.556985
$677$	−40.4980	−1.55647	−0.778233	−	0.627976i	$-0.783884\pi$
$677$	−40.4980	−1.55647	−0.778233	+	0.627976i	$0.783884\pi$
$678$	−91.3154	−3.50695
$679$	4.33074	0.166198
$680$	4.49770	0.172479
$681$	−1.44876	−0.0555168
$682$	0	0
$683$	24.7328	0.946376	0.473188	−	0.880962i	$-0.343103\pi$
$683$	24.7328	0.946376	0.473188	+	0.880962i	$0.343103\pi$
$684$	−18.2562	−0.698041
$685$	19.8048	0.756703
$686$	−1.85511	−0.0708283
$687$	37.1722	1.41821
$688$	−33.2201	−1.26650
$689$	−5.09565	−0.194129
$690$	−5.75341	−0.219029
$691$	30.5516	1.16224	0.581118	−	0.813819i	$-0.302615\pi$
$691$	30.5516	1.16224	0.581118	+	0.813819i	$0.302615\pi$
$692$	30.1160	1.14484
$693$	0	0
$694$	−47.5334	−1.80434
$695$	2.23144	0.0846435
$696$	27.6989	1.04992
$697$	−12.8532	−0.486848
$698$	7.43667	0.281482
$699$	39.7777	1.50453
$700$	−1.44142	−0.0544805
$701$	16.0896	0.607694	0.303847	−	0.952721i	$-0.401729\pi$
$701$	16.0896	0.607694	0.303847	+	0.952721i	$0.401729\pi$
$702$	9.48777	0.358093
$703$	27.4263	1.03440
$704$	0	0
$705$	3.33946	0.125771
$706$	51.3390	1.93217
$707$	−11.0945	−0.417251
$708$	33.1754	1.24681
$709$	11.9695	0.449525	0.224763	−	0.974414i	$-0.427839\pi$
$709$	11.9695	0.449525	0.224763	+	0.974414i	$0.427839\pi$
$710$	−3.79840	−0.142551
$711$	62.0157	2.32577
$712$	−1.21657	−0.0455930
$713$	6.04948	0.226555
$714$	−21.4789	−0.803827
$715$	0	0
$716$	−0.976639	−0.0364987
$717$	5.31051	0.198325
$718$	−1.83966	−0.0686556
$719$	53.0569	1.97869	0.989345	−	0.145592i	$-0.0465087\pi$
$719$	53.0569	1.97869	0.989345	+	0.145592i	$0.0465087\pi$
$720$	−19.7765	−0.737025
$721$	1.06178	0.0395428
$722$	−17.6789	−0.657942
$723$	−51.7656	−1.92519
$724$	31.9426	1.18714
$725$	10.0207	0.372159
$726$	0	0
$727$	47.5190	1.76238	0.881192	−	0.472759i	$-0.156742\pi$
$727$	47.5190	1.76238	0.881192	+	0.472759i	$0.156742\pi$
$728$	−1.78075	−0.0659991
$729$	−41.9593	−1.55405
$730$	6.41348	0.237373
$731$	−30.0074	−1.10986
$732$	−37.8709	−1.39975
$733$	46.3044	1.71029	0.855146	−	0.518387i	$-0.173467\pi$
$733$	46.3044	1.71029	0.855146	+	0.518387i	$0.173467\pi$
$734$	−21.8665	−0.807106
$735$	−2.66752	−0.0983931
$736$	−7.95438	−0.293202
$737$	0	0
$738$	22.6092	0.832257
$739$	−4.47752	−0.164708	−0.0823541	−	0.996603i	$-0.526244\pi$
$739$	−4.47752	−0.164708	−0.0823541	+	0.996603i	$0.526244\pi$
$740$	−12.8463	−0.472241
$741$	−14.1070	−0.518232
$742$	−5.50074	−0.201939
$743$	24.1703	0.886721	0.443360	−	0.896344i	$-0.353786\pi$
$743$	24.1703	0.886721	0.443360	+	0.896344i	$0.353786\pi$
$744$	14.3825	0.527287
$745$	11.6509	0.426856
$746$	22.5333	0.825003
$747$	−72.1654	−2.64039
$748$	0	0
$749$	−18.2462	−0.666703
$750$	−4.94854	−0.180695
$751$	−6.03110	−0.220078	−0.110039	−	0.993927i	$-0.535098\pi$
$751$	−6.03110	−0.220078	−0.110039	+	0.993927i	$0.535098\pi$
$752$	6.01554	0.219364
$753$	36.0690	1.31443
$754$	−31.9458	−1.16340
$755$	3.19583	0.116308
$756$	4.28981	0.156019
$757$	−41.9168	−1.52349	−0.761746	−	0.647875i	$-0.775658\pi$
$757$	−41.9168	−1.52349	−0.761746	+	0.647875i	$0.775658\pi$
$758$	−66.1729	−2.40351
$759$	0	0
$760$	3.18885	0.115672
$761$	0.920467	0.0333669	0.0166834	−	0.999861i	$-0.494689\pi$
$761$	0.920467	0.0333669	0.0166834	+	0.999861i	$0.494689\pi$
$762$	54.5074	1.97459
$763$	7.53824	0.272903
$764$	22.4595	0.812556
$765$	−17.8639	−0.645871
$766$	−61.8867	−2.23606
$767$	14.8274	0.535387
$768$	−55.8631	−2.01579
$769$	26.2133	0.945277	0.472639	−	0.881256i	$-0.343302\pi$
$769$	26.2133	0.945277	0.472639	+	0.881256i	$0.343302\pi$
$770$	0	0
$771$	30.1459	1.08568
$772$	24.0409	0.865250
$773$	1.44103	0.0518303	0.0259151	−	0.999664i	$-0.491750\pi$
$773$	1.44103	0.0518303	0.0259151	+	0.999664i	$0.491750\pi$
$774$	52.7842	1.89729
$775$	5.20319	0.186904
$776$	4.48764	0.161097
$777$	−23.7738	−0.852879
$778$	−61.3287	−2.19874
$779$	−9.11283	−0.326501
$780$	6.60762	0.236591
$781$	0	0
$782$	−9.36164	−0.334772
$783$	−29.8227	−1.06577
$784$	−4.80515	−0.171613
$785$	6.20417	0.221436
$786$	−40.0703	−1.42926
$787$	−8.68426	−0.309560	−0.154780	−	0.987949i	$-0.549467\pi$
$787$	−8.68426	−0.309560	−0.154780	+	0.987949i	$0.549467\pi$
$788$	28.1358	1.00230
$789$	41.2584	1.46884
$790$	27.9530	0.994523
$791$	−18.4530	−0.656113
$792$	0	0
$793$	−16.9260	−0.601061
$794$	−26.5473	−0.942128
$795$	−7.90972	−0.280529
$796$	5.18825	0.183893
$797$	−19.5503	−0.692506	−0.346253	−	0.938141i	$-0.612546\pi$
$797$	−19.5503	−0.692506	−0.346253	+	0.938141i	$0.612546\pi$
$798$	−15.2284	−0.539080
$799$	5.43379	0.192234
$800$	−6.84160	−0.241887
$801$	4.83196	0.170729
$802$	45.0804	1.59184
$803$	0	0
$804$	−1.65122	−0.0582340
$805$	−1.16265	−0.0409780
$806$	−16.5877	−0.584276
$807$	76.6184	2.69710
$808$	−11.4964	−0.404444
$809$	−2.55712	−0.0899036	−0.0449518	−	0.998989i	$-0.514313\pi$
$809$	−2.55712	−0.0899036	−0.0449518	+	0.998989i	$0.514313\pi$
$810$	−8.17770	−0.287335
$811$	−8.11982	−0.285125	−0.142563	−	0.989786i	$-0.545534\pi$
$811$	−8.11982	−0.285125	−0.142563	+	0.989786i	$0.545534\pi$
$812$	−14.4440	−0.506885
$813$	−47.7787	−1.67567
$814$	0	0
$815$	14.8824	0.521308
$816$	−55.6352	−1.94762
$817$	−21.2751	−0.744321
$818$	−10.5471	−0.368772
$819$	7.07276	0.247142
$820$	4.26840	0.149059
$821$	27.3671	0.955120	0.477560	−	0.878599i	$-0.341521\pi$
$821$	27.3671	0.955120	0.477560	+	0.878599i	$0.341521\pi$
$822$	−98.0049	−3.41831
$823$	27.4550	0.957021	0.478511	−	0.878082i	$-0.341177\pi$
$823$	27.4550	0.957021	0.478511	+	0.878082i	$0.341177\pi$
$824$	1.10025	0.0383290
$825$	0	0
$826$	16.0062	0.556926
$827$	−25.5656	−0.889002	−0.444501	−	0.895778i	$-0.646619\pi$
$827$	−25.5656	−0.889002	−0.444501	+	0.895778i	$0.646619\pi$
$828$	6.89731	0.239698
$829$	−20.6733	−0.718013	−0.359006	−	0.933335i	$-0.616884\pi$
$829$	−20.6733	−0.718013	−0.359006	+	0.933335i	$0.616884\pi$
$830$	−32.5279	−1.12906
$831$	−44.4176	−1.54083
$832$	5.29569	0.183595
$833$	−4.34045	−0.150388
$834$	−11.0424	−0.382366
$835$	−15.9864	−0.553232
$836$	0	0
$837$	−15.4852	−0.535248
$838$	−11.4731	−0.396332
$839$	−7.12840	−0.246100	−0.123050	−	0.992400i	$-0.539268\pi$
$839$	−7.12840	−0.246100	−0.123050	+	0.992400i	$0.539268\pi$
$840$	−2.76417	−0.0953728
$841$	71.4144	2.46257
$842$	36.5810	1.26066
$843$	−60.9518	−2.09929
$844$	−30.7397	−1.05811
$845$	−10.0468	−0.345620
$846$	−9.55825	−0.328619
$847$	0	0
$848$	−14.2482	−0.489285
$849$	7.51791	0.258014
$850$	−8.05199	−0.276181
$851$	−10.3619	−0.355200
$852$	7.87280	0.269718
$853$	−14.7303	−0.504354	−0.252177	−	0.967681i	$-0.581147\pi$
$853$	−14.7303	−0.504354	−0.252177	+	0.967681i	$0.581147\pi$
$854$	−18.2716	−0.625242
$855$	−12.6654	−0.433148
$856$	−18.9073	−0.646238
$857$	−26.3568	−0.900330	−0.450165	−	0.892945i	$-0.648635\pi$
$857$	−26.3568	−0.900330	−0.450165	+	0.892945i	$0.648635\pi$
$858$	0	0
$859$	−55.1545	−1.88185	−0.940923	−	0.338621i	$-0.890040\pi$
$859$	−55.1545	−1.88185	−0.940923	+	0.338621i	$0.890040\pi$
$860$	9.96514	0.339809
$861$	7.89921	0.269204
$862$	−72.3419	−2.46397
$863$	−29.3124	−0.997804	−0.498902	−	0.866658i	$-0.666263\pi$
$863$	−29.3124	−0.997804	−0.498902	+	0.866658i	$0.666263\pi$
$864$	20.3613	0.692706
$865$	20.8933	0.710394
$866$	−61.0606	−2.07492
$867$	−4.90690	−0.166647
$868$	−7.49996	−0.254565
$869$	0	0
$870$	−49.5878	−1.68118
$871$	−0.737996	−0.0250060
$872$	7.81135	0.264526
$873$	−17.8239	−0.603249
$874$	−6.63736	−0.224512
$875$	−1.00000	−0.0338062
$876$	−13.2930	−0.449129
$877$	25.4557	0.859577	0.429788	−	0.902930i	$-0.358588\pi$
$877$	25.4557	0.859577	0.429788	+	0.902930i	$0.358588\pi$
$878$	31.1233	1.05036
$879$	16.8544	0.568486
$880$	0	0
$881$	50.4595	1.70002	0.850012	−	0.526763i	$-0.176595\pi$
$881$	50.4595	1.70002	0.850012	+	0.526763i	$0.176595\pi$
$882$	7.63502	0.257085
$883$	1.05108	0.0353717	0.0176859	−	0.999844i	$-0.494370\pi$
$883$	1.05108	0.0353717	0.0176859	+	0.999844i	$0.494370\pi$
$884$	10.7516	0.361614
$885$	23.0158	0.773669
$886$	52.2067	1.75392
$887$	−1.93456	−0.0649563	−0.0324782	−	0.999472i	$-0.510340\pi$
$887$	−1.93456	−0.0649563	−0.0324782	+	0.999472i	$0.510340\pi$
$888$	−24.6351	−0.826699
$889$	11.0148	0.369426
$890$	2.17796	0.0730055
$891$	0	0
$892$	−32.4270	−1.08574
$893$	3.85253	0.128920
$894$	−57.6549	−1.92827
$895$	−0.677555	−0.0226482
$896$	−7.96652	−0.266143
$897$	5.32972	0.177954
$898$	63.7523	2.12744
$899$	52.1396	1.73895
$900$	5.93241	0.197747
$901$	−12.8703	−0.428770
$902$	0	0
$903$	18.4417	0.613703
$904$	−19.1216	−0.635974
$905$	22.1606	0.736642
$906$	−15.8147	−0.525407
$907$	−4.68977	−0.155721	−0.0778606	−	0.996964i	$-0.524809\pi$
$907$	−4.68977	−0.155721	−0.0778606	+	0.996964i	$0.524809\pi$
$908$	0.782852	0.0259798
$909$	45.6614	1.51449
$910$	3.18798	0.105681
$911$	−12.7359	−0.421959	−0.210980	−	0.977490i	$-0.567665\pi$
$911$	−12.7359	−0.421959	−0.210980	+	0.977490i	$0.567665\pi$
$912$	−39.4451	−1.30616
$913$	0	0
$914$	21.8359	0.722268
$915$	−26.2734	−0.868572
$916$	−20.0863	−0.663670
$917$	−8.09741	−0.267400
$918$	23.9636	0.790916
$919$	−10.2363	−0.337664	−0.168832	−	0.985645i	$-0.554000\pi$
$919$	−10.2363	−0.337664	−0.168832	+	0.985645i	$0.554000\pi$
$920$	−1.20477	−0.0397201
$921$	−57.7271	−1.90217
$922$	28.1702	0.927736
$923$	3.51867	0.115818
$924$	0	0
$925$	−8.91230	−0.293035
$926$	−29.0255	−0.953836
$927$	−4.36995	−0.143528
$928$	−68.5576	−2.25051
$929$	−14.6145	−0.479486	−0.239743	−	0.970836i	$-0.577063\pi$
$929$	−14.6145	−0.479486	−0.239743	+	0.970836i	$0.577063\pi$
$930$	−25.7482	−0.844316
$931$	−3.07736	−0.100856
$932$	−21.4942	−0.704066
$933$	−44.0158	−1.44101
$934$	−3.73640	−0.122259
$935$	0	0
$936$	7.32901	0.239556
$937$	−29.5598	−0.965677	−0.482838	−	0.875710i	$-0.660394\pi$
$937$	−29.5598	−0.965677	−0.482838	+	0.875710i	$0.660394\pi$
$938$	−0.796665	−0.0260120
$939$	45.5650	1.48696
$940$	−1.80450	−0.0588564
$941$	−26.6511	−0.868801	−0.434401	−	0.900720i	$-0.643040\pi$
$941$	−26.6511	−0.868801	−0.434401	+	0.900720i	$0.643040\pi$
$942$	−30.7016	−1.00031
$943$	3.44290	0.112116
$944$	41.4596	1.34940
$945$	2.97611	0.0968127
$946$	0	0
$947$	38.6461	1.25583	0.627915	−	0.778282i	$-0.283909\pi$
$947$	38.6461	1.25583	0.627915	+	0.778282i	$0.283909\pi$
$948$	−57.9372	−1.88171
$949$	−5.94117	−0.192859
$950$	−5.70882	−0.185219
$951$	−15.8367	−0.513540
$952$	−4.49770	−0.145771
$953$	1.77004	0.0573373	0.0286687	−	0.999589i	$-0.490873\pi$
$953$	1.77004	0.0573373	0.0286687	+	0.999589i	$0.490873\pi$
$954$	22.6393	0.732974
$955$	15.5815	0.504207
$956$	−2.86957	−0.0928087
$957$	0	0
$958$	4.32301	0.139670
$959$	−19.8048	−0.639531
$960$	8.22023	0.265307
$961$	−3.92686	−0.126673
$962$	28.4122	0.916048
$963$	75.0957	2.41993
$964$	27.9720	0.900917
$965$	16.6786	0.536904
$966$	5.75341	0.185113
$967$	2.62875	0.0845347	0.0422674	−	0.999106i	$-0.486542\pi$
$967$	2.62875	0.0845347	0.0422674	+	0.999106i	$0.486542\pi$
$968$	0	0
$969$	−35.6304	−1.14461
$970$	−8.03398	−0.257955
$971$	37.3711	1.19930	0.599648	−	0.800264i	$-0.295307\pi$
$971$	37.3711	1.19930	0.599648	+	0.800264i	$0.295307\pi$
$972$	29.8191	0.956447
$973$	−2.23144	−0.0715368
$974$	−37.6191	−1.20539
$975$	4.58411	0.146809
$976$	−47.3277	−1.51492
$977$	38.7327	1.23917	0.619585	−	0.784930i	$-0.287301\pi$
$977$	38.7327	1.23917	0.619585	+	0.784930i	$0.287301\pi$
$978$	−73.6462	−2.35495
$979$	0	0
$980$	1.44142	0.0460444
$981$	−31.0250	−0.990552
$982$	−52.6534	−1.68024
$983$	5.10729	0.162897	0.0814486	−	0.996678i	$-0.474045\pi$
$983$	5.10729	0.162897	0.0814486	+	0.996678i	$0.474045\pi$
$984$	8.18540	0.260941
$985$	19.5196	0.621945
$986$	−80.6866	−2.56958
$987$	−3.33946	−0.106296
$988$	7.62280	0.242514
$989$	8.03790	0.255590
$990$	0	0
$991$	−47.5884	−1.51170	−0.755848	−	0.654747i	$-0.772775\pi$
$991$	−47.5884	−1.51170	−0.755848	+	0.654747i	$0.772775\pi$
$992$	−35.5981	−1.13024
$993$	−44.7072	−1.41874
$994$	3.79840	0.120478
$995$	3.59941	0.114109
$996$	67.4194	2.13627
$997$	58.2493	1.84477	0.922386	−	0.386268i	$-0.126236\pi$
$997$	58.2493	1.84477	0.922386	+	0.386268i	$0.126236\pi$
$998$	42.5387	1.34654
$999$	26.5239	0.839180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bk.1.8	yes	10
11.10	odd	2		4235.2.a.bi.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bi.1.3	✓	10	11.10	odd	2
4235.2.a.bk.1.8	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.85511 q^{2} -2.66752 q^{3} +1.44142 q^{4} +1.00000 q^{5} -4.94854 q^{6} -1.00000 q^{7} -1.03623 q^{8} +4.11568 q^{9} +O(q^{10})\)	\(q+1.85511 q^{2} -2.66752 q^{3} +1.44142 q^{4} +1.00000 q^{5} -4.94854 q^{6} -1.00000 q^{7} -1.03623 q^{8} +4.11568 q^{9} +1.85511 q^{10} -3.84501 q^{12} -1.71849 q^{13} -1.85511 q^{14} -2.66752 q^{15} -4.80515 q^{16} -4.34045 q^{17} +7.63502 q^{18} -3.07736 q^{19} +1.44142 q^{20} +2.66752 q^{21} +1.16265 q^{23} +2.76417 q^{24} +1.00000 q^{25} -3.18798 q^{26} -2.97611 q^{27} -1.44142 q^{28} +10.0207 q^{29} -4.94854 q^{30} +5.20319 q^{31} -6.84160 q^{32} -8.05199 q^{34} -1.00000 q^{35} +5.93241 q^{36} -8.91230 q^{37} -5.70882 q^{38} +4.58411 q^{39} -1.03623 q^{40} +2.96125 q^{41} +4.94854 q^{42} +6.91343 q^{43} +4.11568 q^{45} +2.15684 q^{46} -1.25189 q^{47} +12.8179 q^{48} +1.00000 q^{49} +1.85511 q^{50} +11.5782 q^{51} -2.47706 q^{52} +2.96519 q^{53} -5.52099 q^{54} +1.03623 q^{56} +8.20892 q^{57} +18.5895 q^{58} -8.62817 q^{59} -3.84501 q^{60} +9.84936 q^{61} +9.65246 q^{62} -4.11568 q^{63} -3.08159 q^{64} -1.71849 q^{65} +0.429444 q^{67} -6.25640 q^{68} -3.10139 q^{69} -1.85511 q^{70} -2.04754 q^{71} -4.26479 q^{72} +3.45720 q^{73} -16.5333 q^{74} -2.66752 q^{75} -4.43575 q^{76} +8.50402 q^{78} +15.0681 q^{79} -4.80515 q^{80} -4.40821 q^{81} +5.49344 q^{82} -17.5342 q^{83} +3.84501 q^{84} -4.34045 q^{85} +12.8251 q^{86} -26.7304 q^{87} +1.17404 q^{89} +7.63502 q^{90} +1.71849 q^{91} +1.67586 q^{92} -13.8796 q^{93} -2.32240 q^{94} -3.07736 q^{95} +18.2501 q^{96} -4.33074 q^{97} +1.85511 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9} + 2 q^{10} - 4 q^{12} + 18 q^{13} - 2 q^{14} - 4 q^{15} + 4 q^{16} + 4 q^{17} + 12 q^{18} + 14 q^{19} + 12 q^{20} + 4 q^{21} - 4 q^{23} + 46 q^{24} + 10 q^{25} + 2 q^{26} - 34 q^{27} - 12 q^{28} + 36 q^{29} + 8 q^{30} - 18 q^{31} + 4 q^{32} - 32 q^{34} - 10 q^{35} + 22 q^{36} + 4 q^{37} + 18 q^{38} + 6 q^{40} + 38 q^{41} - 8 q^{42} + 6 q^{43} + 14 q^{45} + 28 q^{46} - 18 q^{47} + 16 q^{48} + 10 q^{49} + 2 q^{50} - 4 q^{51} + 26 q^{52} - 26 q^{53} + 2 q^{54} - 6 q^{56} + 22 q^{57} + 10 q^{58} - 14 q^{59} - 4 q^{60} + 60 q^{61} + 22 q^{62} - 14 q^{63} + 18 q^{65} - 10 q^{67} + 2 q^{68} - 8 q^{69} - 2 q^{70} - 54 q^{72} + 18 q^{73} - 20 q^{74} - 4 q^{75} + 38 q^{76} + 40 q^{78} + 40 q^{79} + 4 q^{80} + 18 q^{81} - 36 q^{82} + 2 q^{83} + 4 q^{84} + 4 q^{85} + 42 q^{86} - 32 q^{87} + 2 q^{89} + 12 q^{90} - 18 q^{91} - 64 q^{92} + 26 q^{93} - 68 q^{94} + 14 q^{95} + 28 q^{96} + 8 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 - 4 * q^3 + 12 * q^4 + 10 * q^5 + 8 * q^6 - 10 * q^7 + 6 * q^8 + 14 * q^9 + 2 * q^10 - 4 * q^12 + 18 * q^13 - 2 * q^14 - 4 * q^15 + 4 * q^16 + 4 * q^17 + 12 * q^18 + 14 * q^19 + 12 * q^20 + 4 * q^21 - 4 * q^23 + 46 * q^24 + 10 * q^25 + 2 * q^26 - 34 * q^27 - 12 * q^28 + 36 * q^29 + 8 * q^30 - 18 * q^31 + 4 * q^32 - 32 * q^34 - 10 * q^35 + 22 * q^36 + 4 * q^37 + 18 * q^38 + 6 * q^40 + 38 * q^41 - 8 * q^42 + 6 * q^43 + 14 * q^45 + 28 * q^46 - 18 * q^47 + 16 * q^48 + 10 * q^49 + 2 * q^50 - 4 * q^51 + 26 * q^52 - 26 * q^53 + 2 * q^54 - 6 * q^56 + 22 * q^57 + 10 * q^58 - 14 * q^59 - 4 * q^60 + 60 * q^61 + 22 * q^62 - 14 * q^63 + 18 * q^65 - 10 * q^67 + 2 * q^68 - 8 * q^69 - 2 * q^70 - 54 * q^72 + 18 * q^73 - 20 * q^74 - 4 * q^75 + 38 * q^76 + 40 * q^78 + 40 * q^79 + 4 * q^80 + 18 * q^81 - 36 * q^82 + 2 * q^83 + 4 * q^84 + 4 * q^85 + 42 * q^86 - 32 * q^87 + 2 * q^89 + 12 * q^90 - 18 * q^91 - 64 * q^92 + 26 * q^93 - 68 * q^94 + 14 * q^95 + 28 * q^96 + 8 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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